**(06) Express the following as the sum of two odd primes.**

(a) **44 = 3 + 41** (Both 3 and 41 are odd primes)

(b) ** 36 = 5 + 31** (Both 5 and 31 are odd primes)

(c) ** 24 = 5 + 19 **(Both 5 and 19 are odd primes)

(d)** 18 = 5 + 13** (Both 5 and 13 are odd primes)

**(07) Give three pairs of prime numbers whose difference is 2.**

Sol:

Three pairs of prime numbers whose difference is 2:**a. 5,7b. 11,13 c. 17,19**

In each case, difference between two numbers in a pair is 2.

**(08) Which of the following numbers are prime?**

Sol:

(a) 23 – It has only two factors; 1 and 23, therefore, 23 is a prime number.

(b) 51 – It has more than two factors; 1, 3, 17 and 51, therefore, 51 is not a prime number.

(c) 37 – It has only two factors; 1 and 37, therefore, 37 is a prime number.

(d) 26 – It has more than two factors; 1, 2, 13 and 26, therefore, 26 is not a prime number.

**(09) Write seven consecutive composite numbers less than 100 so that there is no prime number between them.**

Sol:

Seven consecutive numbers less than 100 so that there is no prime number between them are **90, 91, 92, 93, 94, 95 and 96**.

**(10) Express each of the following numbers as the sum of three odd primes:**

Sol:

(a) 21 = 3 + 5 + 13

(b) 31 = 3 + 5 + 23

(c) 53 = 3 + 7 + 43

(d) 61 = 3 + 5 + 53